The present invention relates to a real-time self-compensating gravity gradiometer instrument of the type used to measure local variations in gravity in order to determine the gravity gradient.
Various instruments have been developed to measure gravity, these instruments include gravimeters and gradiometers.
Gravimeters are typically of the uniaxial type and measure the gravity field along the local vertical. A known type of gravimeter uses lasers and a high-precision clock to time a mass (typically, a reflective object) as it falls between two vertically spaced points in an evacuated space. More sophisticated types of these systems as disclosed, for example, in U.S. Pat. No. 5,351,122 to Niebauer et al., use split-beam interferometers to provide increased accuracy.
In contrast, gradiometers measure the differential curvature or ellipticity of gravity equipotential surfaces, the rate of change of the increase of gravity in the horizontal direction, and/or the rate of increase of gravity in the vertical direction.
The above mentioned Niebauer gravimeter can be used to measure the gravity gradient by separating two gravimeters by a known distance xe2x80x9cdxe2x80x9d with the gravity gradient obtained by:
xe2x80x83(g1xe2x88x92g2)/d
Such a multi-gravimeter device is classified as and is referred to as an Absolute Gravity Gradiometer.
Another type of contemporary gravity gradiometer utilizes plural pairs of torque-balance accelerometers that are moved at a constant velocity along an orbital path about a spin axis. Information from each accelerometer at any angular position in the orbit provides information as to the lateral acceleration sensed by the accelerometers.
An exemplary gravity gradiometer suitable for use in the context of the present invention is shown in its basic form in FIG. 9. This gradiometer is sold by the Lockheed Martin corporation (Niagara Falls N.Y. USA) and is described in more detail in U.S. Pat. No. 5,357,802 issued Oct. 25, 1994 to Hofmeyer and Affleck and entitled xe2x80x9cRotating Accelerometer Gradiometer,xe2x80x9d the disclosure of which is incorporated herein by reference.
As shown in FIG. 9, the gravity gradiometer instrument GGI includes eight accelerometers 100 mounted at a common radius and equi-spaced about the periphery of a rotor assembly 102 that is rotated at a constant and controlled angular velocity about a spin axis SA. The rotor assembly 102 includes the rotor 104 carried on a support shaft 106 for rotation therewith. The rotor assembly 102 is rotatably mounted in ball bearings 108 and, in turn, carried in a flex-mount assembly 110. Processing electronics 112 are mounted on the rotor 104 adjacent each accelerometer 100 for processing the respective accelerometer output signal. An inner housing 114 contains the rotor assembly 102 and is designed to rotate with the rotor assembly 102. An outer housing 116 contains the interior components and includes one or more heaters 118 designed to operate the instrument at some controlled temperature above ambient and also includes a magnetic-field shield 120. A slip ring assembly 122 at the upper end of the mounting shaft 106 provides the electrical/signal interface with the rotor assembly 102 and the active devices thereon. A shaft encoder 124 at the lower end of the mounting shaft 106 cooperates with an encoder pick-off 126 to provide rotary position information. The output of the encoder pick-off 126 is provided to a computer and speed controller, which, in turn, controls a drive motor 128 at the upper end of the unit to provide a controlled rotary velocity.
The gradiometer includes an internal linear servo-controlled actuator that imparts a 2 Hz sinusoidal acceleration to each accelerometer pair to enable biasing and compensation of various errors including the g2 rectification error. In addition, the gradiometer is mounted on an external vibration isolation system that a assists in attenuating higher frequency vibration.
Each accelerometer 100 provides a sinusoidally varying analog output that is a function of the acceleration experienced by each accelerometer as the accelerometer orbits the spin axis SA. For a gradiometer having its spin axis SA aligned along the field lines in an ideally uniform and unperturbed gravity field, each accelerometer experiences the same acceleration forces as its proceeds along its orbital path. However, when the local gravity field is perturbed by the presence of one or more masses and/or the spin axis SA is tilted relative to the local vertical field lines, each accelerometer will experience different accelerations throughout its orbit. Gradiometers can be positioned with their spin axis vertical (SAV), their spin axis horizontal (SAH), or at an xe2x80x98umbrellaxe2x80x99 angle in which the spin axis is tilted 35 degrees from the local vertical. The quantitative output of each rotating accelerometer pair, when summed and differenced, can be used to provide information related to the local gravity gradient field.
A gravity gradiometer of the type described above is known as a xe2x80x9crelativexe2x80x9d instrument since the torque-balance accelerometers used in the instrument intrinsically do not measure gravity directly as in the case of a ballistic pendulum or a xe2x80x9cfree-fallxe2x80x9d dropping mass device. The instrument only provides an output voltage or a series digital pulses proportioned to the sensed field as the accelerometer pairs move along their circular orbit about the rotation axis. Additionally, a gradiometer configured with relative measurement accelerometers must be calibrated before field deployment.
Calibration of a gradiometer of this type is effected by introducing a precision, constant rotational rate input which creates a centripetal gravity gradient whose magnitude in Eotvos Units (EU) is given by the approximation "THgr"2/40. The scale factor of the instrument is determined by dividing the signal output of the instrument in either analog volts or digital pulses per second by the computed magnitude of the acceleration gradient. This requires the instrument to be installed in a gyro-stabilized platform where a precision torquing signal is provided to rotate the gravity gradiometer instrument at programmed rates.
Because of the mechanical and electrical instabilities of the linear torque balance accelerometers contained in the rotating accelerometer gradiometer (including time-dependent changes in materials and electrical circuits), the instrument is subject to xe2x80x98driftxe2x80x99 errors by which the instrument goes out of calibration. While, to a certain extent, the drift characteristic for an instrument can be determined and electrically compensated, relative gradiometers used for direct measurement of the gravity gradient must always be monitored (if possible) to determine if they are operating within calibration limits and, of course, re-calibrated periodically.
In contrast, a falling-body gravimeter or gradiometer of the types described above are classified as xe2x80x9cabsolutexe2x80x9d instruments since the measurements are based upon direct application of Newtonian physics (i.e., s=xc2xd(g)t2) and the output of such an instrument is a measure of a fundamental physical constant. Thus, the falling-body gravimeter and/or gradiometer need not be subject to a stringent calibration procedure as required for a rotating-accelerometer gradiometer as described above.
In order for a gradiometer to support natural resource and/or geophysical information, it must have a signal-determining accuracy at least in the one Eotvos Unit range (i.e., 10xe2x88x929 (cm/sec2)/cm or 2.54xc3x9710xe2x88x926 xcexc/inch) or less with a resolution accuracy in the 1-3 pico-g range. Noise sources can arise from within the instrument itself and from sources outside the instrument, especially in those cases where the instrument is mounted on a moving vehicle (i.e. motor vehicle, ship, or aircraft).
Intra-instrument noise, processing errors, and non-linearity sources can include accelerometer scale-factor variations, control loop non-linearities and instabilities, mechanical vibrations arising from motors and bearings, electromagnetic field affects, changes in voltage(s), current flow(s), and the like along with changes consequent to temperature, pressure, and humidity variations. In those cases where the instrument is carried in a moving vehicle, it is not uncommon to mount the instrument in a vibration-isolated, gyro-stabilized platform to provide a measure of inertial stability and to isolate the instrument from the motions and vibrations of the vehicle. As can be appreciated, residual errors, not fully taken out by the gyro-stabilized platform, can also introduce further undesirable effects that affect instrument performance. While substantial efforts have been made to identify error sources and non-linearities and eliminate or minimize these error sources, a real-time gradiometer self-compensation/calibration system has yet to be achieved for a rotating accelerometer gravity gradiometer.
In view of the above, it is an object of the present invention, among others, to provide a real-time self-compensating gravity gradiometer instrument.
It is another object of the present invention to provide a real-time self-compensating gravity gradiometer instrument in which a gravity perturbation of known characteristics functions to compensate the instrument. 0020 In view of these objects, and others, the present invention provides a real-time self-compensating gravity gradiometer instrument in which a known mass concentration is moved in a predictable manner in the instrument near field to provide quantifiable gravity perturbations that affect the instrument output. That portion of the time-varying signal output of the instrument that corresponds to the time-varying perturbations induced by the mass concentration are compared with a pre-determined or pre-calculated time-varying reference function with the difference value between the measured and the pre-calculated functions representing the aggregate or cumulate instrument-specific error contribution to the measured signal. Once this instrument-specific error contribution is determined, the instrument output is subject to a correction or calibration step to remove or otherwise attenuate the instrument-specific error from the gravity measurements to provide an increase in the signal-to-noise ratio.
In its most general form, a known mass concentration is moved along a path in pre-determined manner in the instrument sensing field, preferably its near field, to present a near-field gravity perturbation. The time-varying change in the local gravity field is calculated using Newtonian principles with this calculated value functioning as a calibration or reference standard that is compared with the corresponding signal output of the instrument. The difference between the calculated change in the local gravity field consequent to the movement of the mass concentration and that actually measured by the instrument is a function of the cumulative instrument error contribution. That cumulative instrument error contribution is then used to effect a correction or compensation of the instrument output to provide a more accurate measurement of the desired gravity gradient.
In a preferred form, a mass having known dimensions, density, and center of mass is orbited at a known radius about the instrument sensing axis and in the instrument sensing plane to provide an orbiting near-field gravity perturbation. Since the physical characteristics of the orbiting mass concentration are known, the gravity perturbation caused by the orbiting mass concentration is quantifiable as a time-varying function. That portion of the output signal corresponding to the position-varying gravity perturbation is extracted from the instrument output and compared to the theoretically-determined value; the difference thereof is a function of the aggregation of error sources in the instrument and is used to effect a compensation of the instrument output to increase the signal-to-noise ratio.
The present invention advantageously provides a real-time self-compensating gravity gradiometer instrument in which gravity perturbations of known value are used to maintain instrument calibration.
Other objects and further scope of applicability of the present invention will become apparent from the detailed description to follow, taken in conjunction with the accompanying drawings, in which like parts are designated by like reference characters.